Implications of the statement Acceleration is not relative

[harrylin]

Could you point to (or quote) the specific passage in that reference where Langevin describes using gravity to give a turn-around with zero accelerometer reading?

Sorry for the misunderstanding, I was not clear. It was well known at the time that in free fall all parts of an instrument fall at the same speed, without relative displacement between the parts. That topic is now discussed here: https://www.physicsforums.com/showthread.php?t=674336

 

[harrylin]

The Christoffel symbols do that.

Symbols can't move a body
Compare: http://en.wikipedia.org/wiki/The_Treachery_of_Images

 

[Dale]

Symbols can't move a body

Don't get distracted by the name. The Christoffel symbols are a set of fields. The Christoffel symbols meet all of the requirements you have identified for the "gravitational field".

 

[Dale]

First, an axiom and a postulate:

Physics forums is for discussing mainstream theories only. Personal theories are not permitted. You cannot propose your own axioms or postulates here.

1. As noted above, the rocket coordinates may be chosen without resulting in the movement of the Earth and stars. Selection of the rocket coordinate system does not imply movement of the Earth and stars; therefore the selection of the rocket frame cannot be the cause of the movement of the Earth and stars.

Selection of any specific coordinate system does. I am sorry that you missed the word "specific" in my original statement.

2. A coordinate system is an abstraction, a mere convention used to identify a position in space. A coordinate system is not a physical entity, and therefore cannot be the cause of any physical phenomenon.

Then motion is not a physical phenomenon by this classification. This should not be terribly surprising.

3. If in the rocket frame the selection of the coordinate system is the cause of the increasing distance between Earth and rocket

I was talking about movement, not increasing distance. They are two different things. Movement is a change in position, this is different from a change in distance.

4. If the selection of the coordinate system is the cause, then the firing of the rocket cannot be the cause in the Earth frame.

I think you are still confusing change in position with change in distance.

 

[A.T.]

In my view, a strong case can be made that such an induction cannot bring into being the required gravitational field because, as was pointed out by another, no causal signal can move faster than the speed of light.

If I understand the gravitational field explanation correctly, it boils down to an inertial force that acts in the accelerated frame. In this case the propagation speed argument doesn't apply. Inertial forces are not propagating from A to B, they appear everywhere. And propagation speed limits don't apply to non-inertial frames anyway. For example: When you start rotating, the distant stars quickly reach speeds beyond c in your frame, and they are immediately subject to inertial centrifugal and Coriolis forces.

 

[nitsuj]

Symbols can't move a body
Compare: http://en.wikipedia.org/wiki/The_Treachery_of_Images

lol that's funny.

It's little tough for me to accept Dalespam's wording. But imo it's accurate.

From which perspective is physics described? I would say it is from the perspective of modeling.

And from that perspective I'd say that's a perfect looking pipe.

Pretty sure Dalespam doesn't feel he can power his commute to work with equations. (although indirectly I'd guess he does )

Pretty sure Dalespam could model that commute (and from different observer perspectives) physically.

And if the model is experimentally accurate, what is the difference between the model & what it describes.

 

[Dale]

Einstein definitely referred to a field of force that possesses the property of imparting the same acceleration to all bodies; according to his theory, the gravitation-field generates the accelerated motion.

Just to go back to this statement. Mathematically you can see that the Christoffel symbols is the field which does this. Starting with the previous equation:
$$\frac{d p^{\mu}}{d\tau} = f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} p^{\lambda}$$

Dividing through by the mass we get
$$a^{\mu}=\frac{d u^{\mu}}{d\tau} = \frac{1}{m}f^{\mu} - {\Gamma^{\mu}}_{\nu\lambda} u^{\nu} u^{\lambda}$$

The acceleration imparted by the term with f depends on m, but the acceleration imparted by the term with the Christoffel symbols is the same for all bodies regardless of mass.

 

[GregAshmore]

The text in bold is correct. You are confusing the rocket with a set of coordinates where the rocket is at rest. Or perhaps you are confusing the broad class of coordinate systems where the rocket is at rest with a specific choice of one such coordinate system.

The coordinates simply map events in spacetime to points in R4. If you use a mapping where the Chistoffel symbols at Earth are non zero then Earth accelerates, regardless of whether or not the rocket is firing it's engines or even whether or not the rocket exists. The choice of coordinates determines the Christoffel symbols and therefore the acceleration, not the rocket.

Does this mean that we can put an engine-less pod in space (without gravity due to mass, per the scenario) and then select the appropriate mapping, at will and as needed, to accelerate the Earth and stars until the star of our choice meets up with the pod?

 

[GregAshmore]

[]Are we discussing the validity of the principle of relativity? I thought we were discussing how the (assumed to be valid) principle of relativity is applied to non-inertial observers. That is, I thought you were looking for "laws of physics" that could be applied by *any* observer who assumes himself to be at rest always. I didn't think you were questioning that such laws can exist.

We began by discussing the absoluteness of proper acceleration in the context of the twin paradox. We proceeded to discuss why certain objectors (the one in Taylor & Wheeler, and myself) believe that their objection has not been dealt with. I ended by saying that I am satisfied that the twin paradox is resolved with respect to kinematics, but I am not able to form an opinion with respect to dynamics. So, no, I do not assume that relativity is valid. Specifically, I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

So what makes a claim to be at rest "legitimate"? If the only requirement is the development of one set of equations that can be used by all at-rest observers to correctly predict the behavior of physical systems, then I don't think I have any quarrel with relativity. (I'm past worrying about whether time can vary with velocity.) But if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

I don't necessarily disagree with this, but the only reason I can see for drawing a distinction between the firing of the rocket as "cause" and the force as "result" is that the force is frame-dependent; more precisely, the coordinate acceleration that results from the force is frame-dependent. In other words, you are maintaining that the firing of the rocket is an event that all observers must agree on, but the force is not.

But if there is a frame-independent way of measuring force, or acceleration, this argument fails. And there *is* a frame-independent way of measuring *proper* acceleration (but not coordinate acceleration), as you know. If that's the case, then on what basis do we distinguish the firing of the rocket as "cause" from the proper acceleration as "result"?

Note, again, that I'm not necessarily disagreeing; I'm pointing out what I think is a gap in your argument that needs to be filled. But this question also comes up in relation to "motion"; see further comments below.

I don't know how proper acceleration is calculated. If the calculation has the rocket moving, then the observer in the at-rest rocket will dispute the definition. His claim is that he is absolutely at rest, as explained below.

The way you are stating this, along with the way you are stating your argument as a whole, presupposes that "motion" is something definite and absolute. It's not; it's frame-dependent. What you really should say here is that the stars and the Earth are not moving *relative to each other* (to the approximation we are working with here, anyway).

Similarly, before the rocket fires, Earth and the rocket are not moving *relative to each other*; but after the rocket fires, they are. It is the *relative* motion that needs to be explained; that is the thing that isn't frame-dependent. But your argument tries to explain the "motion of the rocket" or the "motion of the Earth", as if they were absolute. They're not.

It is claimed that motions are not absolute. That must be proven. You know it is true. I do not. I am not required to accept the premise until it is proven. Indeed, I ought not to accept it until it is proven. I am attempting to prove the premise.

The premise is that every observer may legitimately consider himself to be at rest. For the premise to have any meaning at all, "at rest" must mean "absolutely at rest". (Einstein says, "permanently at rest".) Every observer develops the laws of physics on the assumption that he is at rest in absolute space.

If all such observers are able to agree on one set of physical laws ("of the same form"), then the premise that motion is not absolute is proven to be true. If all observers are absolutely at rest, none are. But if just one observer can show that in his circumstances the laws of physics are unique, then the premise is falsified.

In short, if you are going to take as an axiom that the cause must be "physical", then you should also take as an axiom that the *effect* must be physical as well. And since "physical", from the above, basically means "frame-independent"

Your definition of physical assumes the truth of the premise that is to be proven.

neither the motion of the Earth by itself, nor the motion of the rocket by itself, qualify as "effects" that need to be explained. Only the *relative* motion of the Earth and the rocket qualifies.

I disagree. The task is for every resting observer to explain what he sees, expressed as laws of physics. The observer in the resting rocket sees the Earth moving by itself; that is an effect which must be explained.

The whole thing just boils down to: the firing of the rocket causes relative motion of the rocket and the Earth. That's all that's needed.

Not so. The principle of relativity requires the rocket observer to explain how it is that the Earth moves while he remains at rest.

Same comment here: the laws of physics don't talk about the motion of the Earth, or the stars, or the rocket by themselves; they only talk about the *relative* motion of these things with respect to each other.

No again. The principle of relativity requires that the rocket be at rest, which implies that the Earth is moving by itself. The laws of physics must explain the motion of the Earth by itself, and the rocket by itself, if the principle of relativity is true.

If all we need to do is explain the relative motion of the rocket and Earth, I'm good with the force applied to the rocket. There is no reason at all to deal with the headache of induced gravitational fields in flat spacetime. But if the rocket must be allowed to rest, then the Earth must be moving by itself, and the headache must be endured.

I'm not saying I necessarily prefer the "gravitational field" explanation, but the fact that causal signals can't move faster than light (which I brought up before) does not rule out "induction" as a source for the "gravitational field" Einstein talks about. Such an argument, if it were valid, would prove too much: it would prove that ordinary magnetic induction can't exist either. Obviously that's not true.

Consider the analogy with ordinary magnetic induction further. If you try to push a magnet that's in the field of another magnet, the first magnet feels an instant reaction force pushing back; it doesn't have to wait until a light signal has made a round trip to the other magnet. Why not? Because what causes the instant reaction force is not the field produced by the second magnet "right now", but the field produced by the second magnet one light-travel time ago. (For example, if the second magnet is 1 meter away, then the reaction force comes from the field emitted by the second magnet 3.3 nanoseconds ago.)

Similarly, if I am floating in free space and I fire a rocket, I feel a force, normally said to be due to "inertia". But it could also be attributed to the fact that I am in a "gravitational field" produced by the distant stars, just with a time delay; the contribution to the field from Alpha Centauri, say, is from Alpha Centauri as it was 4.3 years ago. The distant stars don't immediately feel any effect from my rocket firing, but I feel an immediate effect because the field at my location has already had plenty of time to propagate from the distant stars.

Einstein says that "a gravitational field appears" when the rocket is fired. Then, "when the clock U1 has reached velocity v the gravitational field disappears."

 

[PeterDonis]

I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

Do you assume that an *inertial* observer can legitimately claim that he is at rest? If so, what's the difference? What makes an inertial observer special?

So what makes a claim to be at rest "legitimate"?

To me the answer is "mu": the question itself presupposes that "at rest" has some absolute meaning. It doesn't; "at rest" is relative. That means the only requirement is indeed this:

If the only requirement is the development of one set of equations that can be used by all at-rest observers to correctly predict the behavior of physical systems, then I don't think I have any quarrel with relativity.

if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

"Real" is too vague a term to be useful here, IMO. Perhaps the term "fictitious" has given a wrong impression:

I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid.

Events are real to all observers. Does that help? For example, if two twins meet up and find that one's clock has less elapsed time than the other's, that's not a "fictitious proceeding". But if one twin says "well, your clock had more elapsed time because you were higher up than me in a gravitational field while my rocket was firing", the gravitational field could be termed "fictitious". But that's more a matter of terminology or interpretation than physics; the traveling twin wants to interpret everything in his "rest frame", but that frame is non-inertial, so physics doesn't look as simple. "Gravitational field" is just a label he puts on the lack of simplicity; but the lack of simplicity is there because of the coordinates he chose. Nothing forces him to use coordinates in which he is always at rest.

It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics.

The stars aren't violating any laws of physics. The actual law is not "things can't travel faster than light"; it is "things can't move outside the local light cones". All of the stars' worldlines are within their local light cones.

Once again, you appear to want to have it both ways; you want the "laws of physics" to look simple, but you want to be able to choose any coordinates you like. You can't have both of those things.

I don't know how proper acceleration is calculated.

You calculate the path curvature of the rocket's worldline. That can be done in any coordinates, including ones in which the rocket is at rest.

It is claimed that motions are not absolute. That must be proven.

How do you want it proven? It has already been shown that "motion" depends on the coordinates you choose. What more do you need?

The premise is that every observer may legitimately consider himself to be at rest. For the premise to have any meaning at all, "at rest" must mean "absolutely at rest".

I disagree; you can't call anything "absolute" if it depends on the coordinates you adopt.

Every observer develops the laws of physics on the assumption that he is at rest in absolute space.

Really? When you're driving your car, do you intuit its physics based on the assumption that you are at rest in absolute space and everything else is moving? If you do, you're pretty unusual; most people talk about "going somewhere" in their car (or walking or bicycling or any other way, for that matter), not "making the grocery store come to me using my car".

If all such observers are able to agree on one set of physical laws ("of the same form"), then the premise that motion is not absolute is proven to be true.

Then it's proven; GR provides just such a set of laws. But in some coordinates, a bunch of the terms in the equations become zero, so the laws look simpler in those coordinates.

Your definition of physical assumes the truth of the premise that is to be proven.

Then give an alternative definition that doesn't make any assumptions relevant to the argument.

The task is for every resting observer to explain what he sees, expressed as laws of physics.

I agree with this. But that doesn't imply this:

The observer in the resting rocket sees the Earth moving by itself; that is an effect which must be explained.

No, the observer in the rocket sees the Earth moving *relative to him*. That's how the laws work. You don't get to declare by fiat that the laws *must* take a certain form, or *must* deal with "absolute rest" or "absolute motion". You have to find out whether they do by finding out what the laws are. It turns out that the actual laws--the laws of GR--do *not* talk about absolute rest or absolute motion; they talk only about relative rest and relative motion. If you want laws that talk about absolute rest and absolute motion, you're going to be disappointed, because there aren't any.

The laws of physics must explain the motion of the Earth by itself, and the rocket by itself, if the principle of relativity is true.

No, the principle of relativity says that *relative* motion is what matters; it says that there is no such thing as absolute motion or absolute rest.

Einstein says that "a gravitational field appears" when the rocket is fired. Then, "when the clock U1 has reached velocity v the gravitational field disappears."

Yes, but he's using the term "gravitational field" in different ways (possibly without realizing it). When he talks about the field being produced by "induction", there *has* to be a time delay involved; but that means there has to be *something* propagating even when the rocket is not firing. That something is the "gravitational field" that is produced by "induction", with the distant stars as the source. When he talks about the field appearing and disappearing, he's using "gravitational field" to mean the force that is felt only when the rocket is firing; but the "field" (the underlying whatever-it-is that produces the induction effect) is there whether or not the rocket is firing.

 

[Dale]

Does this mean that we can put an engine-less pod in space (without gravity due to mass, per the scenario) and then select the appropriate mapping, at will and as needed, to accelerate the Earth and stars until the star of our choice meets up with the pod?

The meeting of worldlines is a frame-invariant geometric fact which cannot be changed through a choice of coordinates.

 

[PAllen]

Specifically, I do not assume that the non-inertial observer in the rocket can legitimately claim that he is at rest throughout. That must be proven.

What do you think of the following:
- The rocket cannot consider themselves inertial. This means that the simplest form of laws of physics cannot be used. A more complex way of expressing laws, that is also true (by natural vanishing of extra terms) for inertial motion, can be used. Thus, if you choose the more complex expression, laws are the same for all motion; however, this in no way changes that inertial and non-inertial motions are in-equivalent.
- The rocket is clearly at rest relative relative to itself. There is no escaping this, so it is clearly a legitimate thing to recognize.

...
But if the requirement is that the observed universe be "real" to every at-rest observer, then I'm not so sure.

What can you possibly mean by this? How can the universe become less real because you are in a rocket firing thrust? I assume this isn't really what you mean, but I am at a loss for what you possibly could mean.

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

I can sympathize with this. Normally, you do not picture that distant mountains move rapidly when you turn your head. However, what would lead to a real problem is trying to apply the simplest form of laws to the 'turning head' frame. The simplest form of laws (only valid in inertial frames) says no matter can travel faster than the speed c. In the turning head frame, there are no limits on coordinate speed; but this law remains in a different way: no matter catches a pulse of light.

I don't know how proper acceleration is calculated. If the calculation has the rocket moving, then the observer in the at-rest rocket will dispute the definition. His claim is that he is absolutely at rest, as explained below.

Proper acceleration calculation has been explained a few times in this thread. I will not repeat. However, I stress that proper acceleration can easily be non-zero for an observer at rest in non-inertial coordinates. As I tried to express it above, the rocket is indisputably at rest relative to itself. However, it is also indisputably non-inertial, which allows proper acceleration to be nonzero for an observer at coordinate rest.

I am not going to address the rest of your post because I am curious to your reaction to the above, first.

 

[stevendaryl]

As I read the posts in this thread regarding what the observer in the resting rocket observes, I saw the word "fictitious" many times. I'm fine with fictitious quantities if they allow me to correctly calculate what is going to happen. (I'm an engineer, not a theoretician.) But if the proceedings seen by the observer in the resting rocket are fictitious, I am not comfortable affirming the statement that all coordinate systems are equally valid. It seems to me that a coordinate system that has the stars violating a law of physics--traveling faster than light speed--has a lesser validity than a coordinate system that has the stars behaving within the laws of physics. The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

The laws of physics are not violated by noninertial coordinates, it's just that they have a different form when they are expressed in noninertial coordinates.

For example, Newton's laws of motion, when described using inertial Cartesian coordinates x and y, look like this:

$\dfrac{d^2 x}{dt^2} = \dfrac{1}{m} F^x$
$\dfrac{d^2 y}{dt^2} = \dfrac{1}{m} F^y$

If we change to a new coordinate system
$r = \sqrt{x^2 + y^2}$
$\theta = arctan(\dfrac{y}{x})$

then the same equations of motion look like this:

$\dfrac{d^2 r}{dt^2} - r (\dfrac{d\theta}{dt})^2 = \dfrac{1}{m} F^{r}$
$\dfrac{d^2 \theta}{dt^2} + \dfrac{2}{r} \dfrac{dr}{dt} \dfrac{d \theta}{dt} = \dfrac{1}{m} F^{\theta}$

They're the same laws of motion, except written in different coordinates. The form of the laws change in different coordinates, but the physical content does not.

Similarly, the rule of light-speed is, in differential form: If an object travels a distance $\delta x$ in time $\delta t$, then

$(c \delta t)^2 - (\delta x)^2 \geq 0$

That's what the law looks like in Cartesian coordinates. In general coordinates, the same law looks like this:

$g_{\mu \nu}\ \delta x^\mu\ \delta x^\nu \geq 0$ (summed over all indices $\mu$ and $\nu$)

where $g_{\mu \nu}$ are the components of the metric tensor in the new coordinate system. In an inertial Cartesian coordinate system, the metric tensor has the simple form

$g_{tt} = c^2$
$g_{xx} = g_{yy} = g_{zz} = -1$
(with all other components zero).

The laws of physics look different in noninertial or curvilinear coordinates, but they have the same physical content.

 

[harrylin]

lol that's funny.

It's little tough for me to accept Dalespam's wording. But imo it's accurate.

From which perspective is physics described? I would say it is from the perspective of modeling. [..]

Somewhat yes; but a physicist never looses sight of the things that he is modelling - in the context of the topic here Einstein also didn't. Never confound physical entities with their mathematical representation.

 

[Dale]

Somewhat yes; but a physicist never looses sight of the things that he is modelling - in the context of the topic here Einstein also didn't. Never confound physical entities with their mathematical representation.

Nobody here is doing that either.

 

[A.T.]

The two coordinate systems may be equally useful, depending on circumstances, but they are not equally valid: one of them is telling a lie about the stars.

You've got it backwards. Frames are preferred based on usefulness, not because some are more valid. For example, if you find it useful to use conservation of momentum, you prefer to use inertial frames, where conservation of momentum applies. But if you don't need conservation of momentum for your calculations, you might prefer some non-inertial frame. The fact that total momentum is not conserved in the non-inertial frame doesn’t make it less valid, just less practical in some cases. Nobody is lying here. Velocity is simply frame dependent.

 

[GregAshmore]

The meeting of worldlines is a frame-invariant geometric fact which cannot be changed through a choice of coordinates.

I'd like a yes or no answer.

After the resting rocket twin fires his engine and sees the Earth accelerate away, he eventually sees his target star approach. He can measure the distance to the star at intervals and verify that it is indeed getting closer. You have said repeatedly that the motion of the Earth is caused by the choice of coordinates, independent of the firing of the rocket. I give you the very same scenario, except without an engine in the rocket. Can you make the very same events happen? Can you cause the Earth and stars to move by selecting a certain coordinate system?

 

[PeterDonis]

I'd like a yes or no answer.

But you've asked two different questions. This actually illustrates well the difference between "motion" and relative motion.

I give you the very same scenario, except without an engine in the rocket. Can you make the very same events happen?

This is question 1. The answer is no: you can't make the very same events happen because you can't change the relative motion of the Earth and the rocket (or the target star and the rocket) without a rocket engine. (We're assuming no other possibilities, i.e., no gravity, no aliens with tractor beams, etc. )

Can you cause the Earth and stars to move by selecting a certain coordinate system?

This is question 2, and is *not* the same as question 1. The answer is yes, of course; just take the coordinate system in which the Earth, the rocket, and the target star are all at rest (since there's no rocket engine, they will always be at rest in this coordinate system), and boost it in some random direction. You now have a coordinate system in which all three are moving, at the same velocity.

What you can't do is get them moving at *different* velocities just by changing coordinate systems. But nobody was claiming that you could; that is, nobody was claiming that you could change their *relative* velocities just by changing coordinates. That's what takes the rocket engine; which is why relative motion is "physical" in a way that "motion" by itself is not.

 

[Mentz114]

Can you cause the Earth and stars to move by selecting a certain coordinate system?

Yes. Any observer moving relative to the Earth and stars will see them moving relative to himself. Velocity is relative.

 

[GregAshmore]

Do you assume that an *inertial* observer can legitimately claim that he is at rest? If so, what's the difference? What makes an inertial observer special?

I don't assume anything with regard to which kind of observer can consider himself at rest. The concept was never of more than passing interest until I read Einstein's book Relativity. I didn't have any pre-conceived ideas going in.

To me the answer is "mu": the question itself presupposes that "at rest" has some absolute meaning. It doesn't; "at rest" is relative. That means the only requirement is indeed this:

I don't think that is true, as a matter of logic. "At rest" must have an absolute meaning for the observer who claims it. Einstein's stated goal was to show that acceleration does not have any absolute quality. Absolute acceleration (as Einstein used the term acceleration in the book referenced above) implies absolute motion. The charge is, "You are accelerating; therefore I am certain that you are in absolute motion." Einstein counters the charge with, "No. I am permanently at rest." For that statement to have any effectiveness against the charge of absolute motion, the rest spoken of must be absolute. If the rest is not absolute, then the observer must admit that he is moving, or at least might be moving. The observer must believe that he is absolutely at rest; he must evaluate all the evidence on the presumption that he is absolutely at rest. You will note that I have not said that any observer is absolutely at rest in actual fact, only that he evaluates what he observes on that basis. So for the resting rocket twin, the Earth moves by itself; the Earth moves absolutely.

I'm going to skip replying to some of your responses. I need more time, and probably more study, to give a good answer.

Events are real to all observers. Does that help? For example, if two twins meet up and find that one's clock has less elapsed time than the other's, that's not a "fictitious proceeding". But if one twin says "well, your clock had more elapsed time because you were higher up than me in a gravitational field while my rocket was firing", the gravitational field could be termed "fictitious". But that's more a matter of terminology or interpretation than physics; the traveling twin wants to interpret everything in his "rest frame", but that frame is non-inertial, so physics doesn't look as simple. "Gravitational field" is just a label he puts on the lack of simplicity; but the lack of simplicity is there because of the coordinates he chose. Nothing forces him to use coordinates in which he is always at rest.

The difference in elapsed clock times is not the issue--not any longer. The issue is whether the rocket twin is moving in some absolute sense, or can legitimately claim to be at rest.

As to why the rocket twin insists on claiming that he is at rest, I guess you'ld have to ask Einstein. I certainly never thought to make an issue of it until I read his book.

Once again, you appear to want to have it both ways; you want the "laws of physics" to look simple, but you want to be able to choose any coordinates you like. You can't have both of those things.

Again, the issue for me is not the simplicity or complexity of the equations. The issue is whether the claim to be at rest makes physical sense. See the end of this post.

You calculate the path curvature of the rocket's worldline. That can be done in any coordinates, including ones in which the rocket is at rest.

Ok. I don't recall seeing this definition before. If it was in this thread, I missed it.

Really? When you're driving your car, do you intuit its physics based on the assumption that you are at rest in absolute space and everything else is moving? If you do, you're pretty unusual; most people talk about "going somewhere" in their car (or walking or bicycling or any other way, for that matter), not "making the grocery store come to me using my car".

In the context, I thought it was clear that I meant every resting observer.

Yes, but he's using the term "gravitational field" in different ways (possibly without realizing it). When he talks about the field being produced by "induction", there *has* to be a time delay involved; but that means there has to be *something* propagating even when the rocket is not firing. That something is the "gravitational field" that is produced by "induction", with the distant stars as the source. When he talks about the field appearing and disappearing, he's using "gravitational field" to mean the force that is felt only when the rocket is firing; but the "field" (the underlying whatever-it-is that produces the induction effect) is there whether or not the rocket is firing.

Prompted by the above, I read this again:

But all the stars that are in the universe, can be conceived as taking part in bringing forth the gravitational field; because during the accelerated phases of the coordinate system K' they are accelerated relative to the latter and thereby can induce a gravitational field, similar to how electric charges in accelerated motion can induce an electric field.

This is consistent with the idea that the field is present all the time. But there seems to be a causal conundrum here. The effect of the field is not felt until the Earth accelerates. But the Earth only accelerates due to the effect of the field.

If no plausible explanation for the workings of the gravitational field can be given, the field must be considered a pure fiction; ad-hoc hand-waving. In that case, the absoluteness of acceleration is not removed, at least with respect to SR.

Personally, I have no stake in the argument. I don't care if there is an absoluteness to acceleration. But the issue was important to Einstein, and having come this far, I'd like to be able to evaluate whether he succeeded in eliminating the problem.

 

[Mentz114]

If no plausible explanation for the workings of the gravitational field can be given, the field must be considered a pure fiction; ad-hoc hand-waving. In that case, the absoluteness of acceleration is not removed, at least with respect to SR.

Gravity produces coordinate acceleration but rockets produce proper acceleration. The field that Einstein conjures up produces the first kind - which is relative. But, as you have been told, proper acceleration is not coordinate dependent and cannot be made to disappear or appear by a change of coordinates. Proper acceleration is absolute in this sense.

Personally, I have no stake in the argument. I don't care if there is an absoluteness to acceleration. But the issue was important to Einstein, and having come this far, I'd like to be able to evaluate whether he succeeded in eliminating the problem.

Again, it's been said before, Einstein does not make it clear which kind he refers to so he has not succeeded, in my opinion.

 

[PeterDonis]

I don't assume anything with regard to which kind of observer can consider himself at rest.

Then we're missing a big piece of the puzzle, because we haven't established, have we, that the principle of relativity applies to *inertial* observers? If we haven't even done that, how can we do it for non-inertial observers?

I don't think that is true, as a matter of logic. "At rest" must have an absolute meaning for the observer who claims it.

How can it be absolute if it's only true for the observer who claims it? Doesn't that make it relative? Isn't that the whole *point* of making the distinction between "relative" and "absolute"?

Einstein's stated goal was to show that acceleration does not have any absolute quality.

Just like "motion" and "rest". That was his whole point. He wasn't trying to argue that motion or rest were absolute. If you think he was arguing that, you have seriously misunderstood his point.

The charge is, "You are accelerating; therefore I am certain that you are in absolute motion." Einstein counters the charge with, "No. I am permanently at rest."

No, you're misunderstanding what he said. A better statement of his counter is: "No. There is no such thing as absolute motion. Acceleration, like motion and rest, is relative." Then he investigates what it takes to consistently maintain such a position, and finds out that to do so, we must also accept that a "gravitational field" (in the sense of "acceleration due to gravity"--mathematically, as DaleSpam pointed out, this corresponds to Christoffel symbols, first derivatives of the metric) is relative; it can be present in some frames and absent in others.

In the context, I thought it was clear that I meant every resting observer.

Huh? The position you have been taking is that *every* observer can consider himself to be at rest, so "resting observer" just means any observer whatsoever. *I* can draw distinctions like the one I drew in what you quoted--nobody in real life considers himself to be "at rest" and the grocery store to be moving--because I'm arguing that relative motion is what's important anyway. But how can *you* draw such distinctions without undermining your whole position?

The effect of the field is not felt until the Earth accelerates. But the Earth only accelerates due to the effect of the field.

No, the effect of the field is always there. When the rocket engine is off, the rocket and the person inside are free-falling in the field along with the Earth. When the rocket engine fires, it holds the rocket and the person inside at rest in the field so they can't free-fall with the Earth. So the Earth appears to accelerate "downward". But the field is always there; firing the rocket engine just prevents the rocket from free-falling in it.

 

[GregAshmore]

What do you think of the following:

My reply will have to wait until tomorrow night.

 

[Dale]

I'd like a yes or no answer.

OK

Does this mean that we can put an engine-less pod in space (without gravity due to mass, per the scenario) and then select the appropriate mapping, at will and as needed, to accelerate the Earth and stars until the star of our choice meets up with the pod?

No.

After the resting rocket twin fires his engine and sees the Earth accelerate away, he eventually sees his target star approach. He can measure the distance to the star at intervals and verify that it is indeed getting closer. You have said repeatedly that the motion of the Earth is caused by the choice of coordinates, independent of the firing of the rocket. I give you the very same scenario, except without an engine in the rocket. Can you make the very same events happen?

No.

Can you cause the Earth and stars to move by selecting a certain coordinate system?

Yes.

 

[A.T.]

If no plausible explanation for the workings of the gravitational field can be given, the field must be considered a pure fiction

All of physics is that kind of "fiction". But it is "fiction" that describes nature quantitatively and allows predictions. Newton didn't explain the workings of his gravitational field either. He just quantified it, and this "fiction" still works great for most purposes.

 

[GregAshmore]

The laws of physics are not violated by noninertial coordinates, it's just that they have a different form when they are expressed in noninertial coordinates.

For example, Newton's laws of motion, when described using inertial Cartesian coordinates x and y, look like this:

$\dfrac{d^2 x}{dt^2} = \dfrac{1}{m} F^x$
$\dfrac{d^2 y}{dt^2} = \dfrac{1}{m} F^y$

If we change to a new coordinate system
$r = \sqrt{x^2 + y^2}$
$\theta = arctan(\dfrac{y}{x})$

then the same equations of motion look like this:

$\dfrac{d^2 r}{dt^2} - r (\dfrac{d\theta}{dt})^2 = \dfrac{1}{m} F^{r}$
$\dfrac{d^2 \theta}{dt^2} + \dfrac{2}{r} \dfrac{dr}{dt} \dfrac{d \theta}{dt} = \dfrac{1}{m} F^{\theta}$

They're the same laws of motion, except written in different coordinates. The form of the laws change in different coordinates, but the physical content does not.

True, the physical content does not change in this example.

The laws of physics look different in noninertial or curvilinear coordinates, but they have the same physical content.

This is not true in the case of the resting rocket. In that coordinate system, no force acts on the Earth, yet it accelerates. And, an unbalanced force acts on the rocket, yet it does not accelerate. Both of these phenomena violate Newton's law as quoted above. Additional physical content is proposed as an explanation: a gravitational field. Additional term(s) are needed in the equation to express the behavior of the additional physical content. I believe (but can't say for sure) that the equation presented by DaleSpam in #278 corresponds to the law of Newton quoted above, with the addition of Christoffel symbols to account for the gravitational field.

 

[GregAshmore]

What do you think of the following:
- The rocket cannot consider themselves inertial. This means that the simplest form of laws of physics cannot be used. A more complex way of expressing laws, that is also true (by natural vanishing of extra terms) for inertial motion, can be used. Thus, if you choose the more complex expression, laws are the same for all motion; however, this in no way changes that inertial and non-inertial motions are in-equivalent.
- The rocket is clearly at rest relative relative to itself. There is no escaping this, so it is clearly a legitimate thing to recognize.

Yes to both points.

What can you possibly mean by this? How can the universe become less real because you are in a rocket firing thrust? I assume this isn't really what you mean, but I am at a loss for what you possibly could mean.

The universe as depicted by the observer in the resting rocket has a homogenous gravitational field of vaguely specified origin. That gravitational field is necessary to maintain the claim that the rocket is really at rest. The reality of this gravitational field is questionable; hence the reality of the universe that contains it is questionable.

I can sympathize with this. Normally, you do not picture that distant mountains move rapidly when you turn your head. However, what would lead to a real problem is trying to apply the simplest form of laws to the 'turning head' frame. The simplest form of laws (only valid in inertial frames) says no matter can travel faster than the speed c. In the turning head frame, there are no limits on coordinate speed; but this law remains in a different way: no matter catches a pulse of light.

Ok. Still, one must remember that certain measurements cannot be trusted as valid at face value. It wouldn't do for someone at rest in such a coordinate system to insist, based on his measurements, that the universe does allow objects to travel at speeds greater than c. That universe would not be real.

Proper acceleration calculation has been explained a few times in this thread. I will not repeat. However, I stress that proper acceleration can easily be non-zero for an observer at rest in non-inertial coordinates. As I tried to express it above, the rocket is indisputably at rest relative to itself. However, it is also indisputably non-inertial, which allows proper acceleration to be nonzero for an observer at coordinate rest.

Yes. But if by pointing this out you mean to say that non-zero proper acceleration implies "actual" or "real" or "absolute" acceleration, the resting rocket observer is under no obligation to concede the point. He acknowledges that he was non-inertial; he does not acknowledge that he accelerated. Is there any physical evidence that will compel him to acknowledge that he accelerated?

 

[GregAshmore]

All of physics is that kind of "fiction". But it is "fiction" that describes nature quantitatively and allows predictions. Newton didn't explain the workings of his gravitational field either. He just quantified it, and this "fiction" still works great for most purposes.

Fiction to some degree perhaps. But there are surely degrees of fiction. Newton could point to specific massive bodies and specific distances between them to explain the cause of specific gravitational effects. That kind of detail is missing from the explanation for the behavior of the resting rocket.

 

[GregAshmore]

Gravity produces coordinate acceleration but rockets produce proper acceleration. The field that Einstein conjures up produces the first kind - which is relative. But, as you have been told, proper acceleration is not coordinate dependent and cannot be made to disappear or appear by a change of coordinates. Proper acceleration is absolute in this sense.

Is the argument for absolute acceleration compelling? The physical phenomenon that is indisputably present in all coordinate systems is the unbalanced force. The physical reality of the worldline path is not an indisputable fact in any coordinate system, as I understand the concept. The rocket observer acknowledges that he is non-inertial; he sees the non-zero reading on his accelerometer. To him, this indicates an unbalanced force, and nothing more. He can say, "I would have accelerated if I hadn't been held back by the gravitational field." I don't see how an appeal to the worldline can overcome this objection. In short, assuming that his gravitational field is plausible, all he is compelled to recognize are the measurements that are made by the instruments in his coordinate system. Those measurements do not indicate that he moved.

 

[Mentz114]

Is the argument for absolute acceleration compelling?

You must say whether you mean proper or coordinate acceleration. I've nothing to add to what I said about the transformation of proper acceleration.

The physical phenomenon that is indisputably present in all coordinate systems is the unbalanced force.

I don't know what an 'unbalanced' force is. Presumably one that meets no resistance. But it is the inertial resistance of the rocket to its engine thrust that balances the rocket thrust. And that can't be transformed away.

The physical reality of the worldline path is not an indisputable fact in any coordinate system, as I understand the concept.

I have to disagree. The worldlines of the involved parties are *actually* what happens, and the physics they contain is coordinate independent. For instance, worldlines crossing, or approaching or separating are facts that cannot be changed by transformations. A worldline is an itinerary - it tells us where and when the object is.

The rocket observer acknowledges that he is non-inertial; he sees the non-zero reading on his accelerometer. To him, this indicates an unbalanced force, and nothing more. He can say, "I would have accelerated if I hadn't been held back by the gravitational field." I don't see how an appeal to the worldline can overcome this objection. In short, assuming that his gravitational field is plausible, all he is compelled to recognize are the measurements that are made by the instruments in his coordinate system. Those measurements do not indicate that he moved.

Sorry, I don't get the point of this bit.
We can find coordinates in which the rocket observer is at rest, but ( to him ) the things around him will appear to be moving.

Reading some of your ither replies - I think you are still a bit confused. You ask

Is there any physical evidence that will compel him to acknowledge that he accelerated?

Obviously there is. He will feel his weight and the accelerometer shows a reading. Inescapable evidence of acceleration. Motion is relative, so acceleration is not evidence of motion. You seem to think that because something feels acceleration, it must also change it's state of motion. But an object at rest in the Earth's field still feels acceleration, so acceleration can also make something stop moving ( in a certain frame ).

 

[GregAshmore]

OK

No.

No.

Yes.

Back to the original scenario.

1. Prior to the firing of the rocket, if you select the specific coordinate system, do you make both the Earth and the rocket move, and in such a way as to maintain unchanged the distance between them?

If the answer to 1 is yes, please go on.

2. If you repeatedly select and deselect the specific coordinate system prior to the firing of the rocket, will the result each time be the same as in 1, making both the Earth and the rocket move, and in such a way as to maintain unchanged the distance between them?

3. If you select the specific coordinate system during the firing of the rocket:
3a: Will you make the Earth move?
3b: Will you make the rocket move?

 

[GregAshmore]

You must say whether you mean proper or coordinate acceleration. I've nothing to add to what I said about the transformation of proper acceleration.

My question is whether the resting rocket observer is compelled by any evidence to accept that he accelerated.

I don't know what an 'unbalanced' force is. Presumably one that meets no resistance. But it is the inertial resistance of the rocket to its engine thrust that balances the rocket thrust. And that can't be transformed away.

It's tough to satisfy everyone on the forum. I once said "force" unqualified, meaning a force that would cause acceleration as judged from an inertial frame, and was corrected for being ambiguous.

I have to disagree. The worldlines of the involved parties are *actually* what happens, and the physics they contain is coordinate independent. For instance, worldlines crossing, or approaching or separating are facts that cannot be changed by transformations.

What hard evidence do you have that there is such a thing as a wordline? I've spent thousands of hours working with accelerating masses; I've never seen any evidence of such a thing.

Sorry, I don't get the point of this bit.
We can find coordinates in which the rocket observer is at rest, but the things around him will appear to be moving in complicated way.

When you tell the resting rocket observer that he is absolutely accelerating, it makes no difference to him whether you say "proper" or "coordinate" acceleration. Acceleration implies movement. The fact that the movement (distance traversed) is shown on a worldline instead of in his coordinates does not change the fact that you are claiming that he moved. He denies movement.

Obviously there is. He will feel his weight and the accelerometer shows a reading. Inescapable evidence of acceleration.

Really? I deny it. It is inescapable evidence that I am being pushed against my seat. It is not evidence that my seat is moving.

 

[Mentz114]

My question is whether the resting rocket observer is compelled by any evidence to accept that he accelerated.

I thought I answered that.

What hard evidence do you have that there is such a thing as a wordline? I've spent thousands of hours working with accelerating masses; I've never seen any evidence of such a thing.

Have a look at this
http://en.wikipedia.org/wiki/World_line

When you tell the resting rocket observer that he is absolutely accelerating, it makes no difference to him whether you say "proper" or "coordinate" acceleration.

Yes it does. With no proper acceleration there is no weight or accelerometer reading. An object can accelerate towards the Earth and be weightless.

Acceleration implies movement.

Movement is relative. Acceleration does not always imply movement.

The fact that the movement (distance traversed) is shown on a worldline instead of in his coordinates does not change the fact that you are claiming that he moved. He denies movement.

I thought you didn't believe in worldlines

Really? I deny it. It is inescapable evidence that I am being pushed against my seat. It is not evidence that my seat is moving.

I did not say it was such eveidnce. I've tried really hard to make the point that acceleration is not evidence of movement. You keep saying it, though.

Everybody is always moving according to some observer somewhere. Movement is relative.

Anyhow, I have to quit now.

 

[Dale]

The questions, as asked, are unanswerable. I have modified them as little as possible to make them answerable.

1. Prior to the firing of the rocket, if you select the specific coordinate system, [STRIKE]do[/STRIKE] can you make both the Earth and the rocket move, and in such a way as to maintain unchanged the distance between them?

Yes.

2. If you repeatedly select and deselect the specific coordinate system prior to the firing of the rocket, [STRIKE]will[/STRIKE] can the result each time be the same as in 1, making both the Earth and the rocket move, and in such a way as to maintain unchanged the distance between them?

Yes

3. If you select the specific coordinate system during the firing of the rocket:
3a: [STRIKE]Will[/STRIKE] can you make the Earth move?

Yes.

3b: [STRIKE]Will[/STRIKE] Can you make the rocket move?

Yes.

You have enormous flexibility in choosing coordinate systems. You can choose charts such that each of those statements is true. You can also choose charts such that each is false.

 

[GregAshmore]

I thought I answered that.


Have a look at this
http://en.wikipedia.org/wiki/World_line


Yes it does. With no proper acceleration there is no weight or accelerometer reading. An object can accelerate towards the Earth and be weightless.


Movement is relative. Acceleration does not always imply movement.


I thought you didn't believe in worldlines


I did not say it was such eveidnce. I've tried really hard to make the point that acceleration is not evidence of movement. You keep saying it, though.

Everybody is always moving according to some observer somewhere. Movement is relative.

Anyhow, I have to quit now.

The bolded text highlights our disagreement. You say that acceleration does not imply movement. I say that the definition of acceleration implies movement; by definition, there is no acceleration without movement.

As I understand your position, the distinction between coordinate acceleration and proper acceleration allows you to say that there can be acceleration without movement. That position cannot withstand logical scrutiny.

I begin with a caveat:
The definition of proper acceleration has been given as "calculated along the path of the worldline." This definition is ambiguous because it does not define how the worldline is constructed.

In this thread several methods for constructing the worldline of the rocket have been proposed. One of these had the rocket at the same position throughout, so the acceleration along that path would be zero. Obviously, that cannot be the method that is to be used.

Whatever the method that is to be is to be used, the path along the worldline must have non-zero length; the worldline must show the rocket as having traveled some distance. (I suppose that the worldline of the rocket is to be drawn with reference to an inertial frame, but that is not necessary for the success of my argument.)

Here is my logic:
1. An absolute quantity cannot be dependent on a non-absolute quantity.
2. Proper acceleration is absolute.
3. Proper acceleration is derived from, and therefore dependent on, proper velocity.
4. It follows that proper velocity is absolute.
5. Proper velocity is derived from, and therefore dependent on, the distance traveled along the worldline.
6. It follows that the distance traveled along the worldline is absolute.
7. The distance traveled along the worldine is, by definition, the distance through spacetime traveled by the rocket.
8. A "distance traveled" is by definition "movement".
9. It follows that the rocket has experienced absolute movement through spacetime.

[Aside: I have seen the terms "proper acceleration" and "proper velocity" in this thread. I have not seen the term "proper distance." It seems to me that "proper distance" is the appropriate term for the distance through spacetime traveled by the rocket.]

When you tell the resting rocket observer that he had proper acceleration, you are also telling him that he moved some absolute distance through spacetime. That is precisely the charge he intended to deny when he made the claim to be permanently at rest.

From the wikipedia article you referenced:

The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" (such as an orbit in space or a trajectory of a truck on a road map) by the time dimension, and typically encompasses a large area of spacetime wherein perceptually straight paths are recalculated to show their (relatively) more absolute position states — to reveal the nature of special relativity or gravitational interactions.

Personally, I am much more inclined to accept the argument for relative motion through absolute space than to accept the argument for a gravitational field that holds the rocket still while its engine is firing. Even so, the notion of absolute space is an abstraction. The resting observer in the rocket is not compelled by any direct evidence to acknowledge the reality of that abstraction.